Existence and Dimension Properties of a Global B-Pullback Attractor for a Cocycle Generated by a Discrete Control System

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Existence and Dimension Properties of a Global B-Pullback Attractor for a Cocycle Generated by a Discrete Control System. / Maltseva, A. A.; Reitmann, V.

In: Differential Equations, Vol. 53, No. 13, 01.12.2017, p. 1703-1714.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{979fdf04595044dcb57c2f1577b4e841,

title = "Existence and Dimension Properties of a Global B-Pullback Attractor for a Cocycle Generated by a Discrete Control System",

abstract = "We consider cocycles on finite-dimensional manifolds generated by discrete-time control systems. Frequency conditions for the existence of a global B-pullback attractor for such cocycles considered over a general base system on a metric space are given. Upper bounds for the Hausdorff dimension of the global B-pullback attractor of a discrete cocycle are obtained using the transfer function of the linear part of the cocycle and the discrete Kalman–Yakubovich–Popov frequency theorem.",

author = "Maltseva, {A. A.} and V. Reitmann",

note = "Funding Information: This work was supported by the Russian Science Foundation grant no. 14-21-00041 and by the German Academic Exchange Service (DAAD). Publisher Copyright: {\textcopyright} 2017, Pleiades Publishing, Ltd. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

year = "2017",

month = dec,

day = "1",

doi = "10.1134/S001226611713002X",

language = "English",

volume = "53",

pages = "1703--1714",

journal = "Differential Equations",

issn = "0012-2661",

publisher = "Pleiades Publishing",

number = "13",

}

RIS

TY - JOUR

T1 - Existence and Dimension Properties of a Global B-Pullback Attractor for a Cocycle Generated by a Discrete Control System

AU - Maltseva, A. A.

AU - Reitmann, V.

N1 - Funding Information: This work was supported by the Russian Science Foundation grant no. 14-21-00041 and by the German Academic Exchange Service (DAAD). Publisher Copyright: © 2017, Pleiades Publishing, Ltd. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - We consider cocycles on finite-dimensional manifolds generated by discrete-time control systems. Frequency conditions for the existence of a global B-pullback attractor for such cocycles considered over a general base system on a metric space are given. Upper bounds for the Hausdorff dimension of the global B-pullback attractor of a discrete cocycle are obtained using the transfer function of the linear part of the cocycle and the discrete Kalman–Yakubovich–Popov frequency theorem.

AB - We consider cocycles on finite-dimensional manifolds generated by discrete-time control systems. Frequency conditions for the existence of a global B-pullback attractor for such cocycles considered over a general base system on a metric space are given. Upper bounds for the Hausdorff dimension of the global B-pullback attractor of a discrete cocycle are obtained using the transfer function of the linear part of the cocycle and the discrete Kalman–Yakubovich–Popov frequency theorem.

UR - http://www.scopus.com/inward/record.url?scp=85044169234&partnerID=8YFLogxK

U2 - 10.1134/S001226611713002X

DO - 10.1134/S001226611713002X

M3 - Article

AN - SCOPUS:85044169234

VL - 53

SP - 1703

EP - 1714

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 13

ER -

ID: 73405801